Graphs with convex domination number close to their order

Access Full Article

Abstract

top
For a connected graph G = (V,E), a set D ⊆ V(G) is a dominating set of G if every vertex in V(G)-D has at least one neighbour in D. The distance dG(u,v) between two vertices u and v is the length of a shortest (u-v) path in G. An (u-v) path of length dG(u,v) is called an (u-v)-geodesic. A set X ⊆ V(G) is convex in G if vertices from all (a-b)-geodesics belong to X for any two vertices a,b ∈ X. A set X is a convex dominating set if it is convex and dominating. The convex domination number γcon(G) of a graph G is the minimum cardinality of a convex dominating set in G. Graphs with the convex domination number close to their order are studied. The convex domination number of a Cartesian product of graphs is also considered.

@article{JoannaCyman2006, abstract = {For a connected graph G = (V,E), a set D ⊆ V(G) is a dominating set of G if every vertex in V(G)-D has at least one neighbour in D. The distance $d_G(u,v)$ between two vertices u and v is the length of a shortest (u-v) path in G. An (u-v) path of length $d_G(u,v)$ is called an (u-v)-geodesic. A set X ⊆ V(G) is convex in G if vertices from all (a-b)-geodesics belong to X for any two vertices a,b ∈ X. A set X is a convex dominating set if it is convex and dominating. The convex domination number $γ_\{con\}(G)$ of a graph G is the minimum cardinality of a convex dominating set in G. Graphs with the convex domination number close to their order are studied. The convex domination number of a Cartesian product of graphs is also considered.}, author = {Joanna Cyman, Magdalena Lemańska, Joanna Raczek}, journal = {Discussiones Mathematicae Graph Theory}, keywords = {convex domination; Cartesian product}, language = {eng}, number = {2}, pages = {307-316}, title = {Graphs with convex domination number close to their order}, url = {http://eudml.org/doc/270504}, volume = {26}, year = {2006},}

TY - JOURAU - Joanna CymanAU - Magdalena LemańskaAU - Joanna RaczekTI - Graphs with convex domination number close to their orderJO - Discussiones Mathematicae Graph TheoryPY - 2006VL - 26IS - 2SP - 307EP - 316AB - For a connected graph G = (V,E), a set D ⊆ V(G) is a dominating set of G if every vertex in V(G)-D has at least one neighbour in D. The distance $d_G(u,v)$ between two vertices u and v is the length of a shortest (u-v) path in G. An (u-v) path of length $d_G(u,v)$ is called an (u-v)-geodesic. A set X ⊆ V(G) is convex in G if vertices from all (a-b)-geodesics belong to X for any two vertices a,b ∈ X. A set X is a convex dominating set if it is convex and dominating. The convex domination number $γ_{con}(G)$ of a graph G is the minimum cardinality of a convex dominating set in G. Graphs with the convex domination number close to their order are studied. The convex domination number of a Cartesian product of graphs is also considered.LA - engKW - convex domination; Cartesian productUR - http://eudml.org/doc/270504ER -